Markowitz Portfolio Theory Helps Decrease Medicines’ Side Effect and Speed Up Machine Learning

In this paper, we show that, similarly to the fact that distributing the investment between several independent financial instruments decreases the investment risk, using a combination of several medicines can decrease the medicines’ side effects. Moreover, the formulas for optimal combinations of medicine are the same as the formulas for the optimal portfolio, formulas first derived by the Nobel-prize winning economist H. M. Markowitz. A similar application to machine learning explains a recent success of a modified neural network in which the input neurons are also directly connected to the output ones. 1 Markowitz Portfolio Theory: A Brief Reminder The main idea behind Markowitz portfolio theory. In his Nobel-prize winning paper [5], H. M. Markowitz proposed a method for selecting an optimal portfolio of financial investments. To be explain the main ideas behind his method, let us start with a simple case when we have n independent financial instrument, each with a known expected return-on-investment μi and a known standard deviation σi. In principle, we can combine these portfolios, by allocating the part wi of our investment amount to the i-th instrument. Here, we have wi ≥ 0 and n ∑ i=1 wi = 1. For each of these portfolios, we can determine the expected return on investment μ and the standard deviation σ from the formulas Thongchai Dumrongpokaphan Faculty of Science, Chiang Mai University, Chiang Mai, Thailand, e-mail: [email protected] Vladik Kreinovich Department of Computer Science, University of Texas at El Paso, 500 W. University El Paso, Texas 79968, USA, e-mail: [email protected]